A230350 Number of permutations of [2n+10] in which the longest increasing run has length n+10.

1, 22, 491, 12032, 328950, 10027440, 339006360, 12628788480, 515033719200, 22855760928000, 1097589192336000, 56754471481344000, 3145763658989952000, 186150029203211673600, 11717355323144959488000, 781981263963810054144000, 55165533654753963657216000

Offset: 0

Author

Alois P. Heinz, Oct 16 2013

Keywords

• nonn

Comments

Also the number of ascending runs of length n+10 in the permutations of [2n+10].

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..300

Crossrefs

A diagonal of A008304, A122843.

Programs

Maple

a:= proc(n) option remember; `if`(n<2, 1+21*n, 2*(n+5)*(2*n+9)*
      (n^3+22*n^2+132*n+131)*a(n-1)/((n+12)*(n^3+19*n^2+91*n+20)))
    end:
seq(a(n), n=0..25);

Formula

a(n) = (n^3+22*n^2+132*n+131)*(2*n+10)!/(n+12)! for n>0, a(0) = 1.

a(n) = A008304(2*n+10,n+10) = A122843(2*n+10,n+10).